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This version (29 Jul 2020 19:53) was approved by dmercer.The Previously approved version (20 Oct 2018 16:15) is available.Diff

Activity : Voltage and Current Division

Objective:

The objective of this Lab activity is to verify the voltage and current division properties of resistor networks.

Notes:

As in all the ALM labs we use the following terminology when referring to the connections to the ALM1000 connector and configuring the hardware. The green shaded rectangles indicate connections to the M1000 analog I/O connector. The analog I/O channel pins are referred to as CA and CB. When configured to force voltage / measure current -V is added as in CA-V or when configured to force current / measure voltage -I is added as in CA-I. When a channel is configured in the high impedance mode to only measure voltage -H is added as CA-H.

Scope traces are similarly referred to by channel and voltage / current. Such as CA-V , CB-V for the voltage waveforms and CA-I , CB-I for the current waveforms.

Background:

Voltage and Current division allow us to simplify the task of analyzing a circuit. Voltage Division allows us to calculate what fraction of the total voltage across a series string of resistors is dropped across any one resistor. For the circuit of figure 1, the Voltage Division formulas are:

V_1 =  V_S R_1/(R_1 + R_2) (1)

V_2 = V_S R_2/(R_1 + R_2) (2)

Figure 1. Voltage division

Current Division allows us to calculate what fraction of the total current into a parallel string of resistors flows through any one of the resistors.

Figure 2, Current division

For the circuit of figure 2, the Current Division formulas are:

I_1 = I_S R_2/(R_1 + R_2) (3)

I_2 = I_S R_1/(R_1 + R_2) (4)

Materials:

ADALM1000 hardware module
Various Resistors 470 Ω, 1 KΩ, 4.7 KΩ. and 1.5 KΩ

Procedure:

1. Verifying the voltage division:

a) Construct the circuit as shown in figure 1. Set R1= 4.7 KΩ, R2= 1.5 KΩ and use the fixed power supply 5V as voltage source Vs. Use the Volt Meter Tool to measure the voltages V1 and V2

Repeat this step for R1 = R2 = 4.7 KΩ. and write down the measurements.

b) Calculate the voltages V1 and V2 by using the formulas (1) and (2) in each case.

c) Compare the results from steps 1a and 1b.

2. Verifying the current division:

a) Construct the circuit as shown in figure 2. Set R1= 470 Ω, R2= 1 KΩ. and Rs=470 Ω. Use the Meter Source tool to measure the currents Is, I1 and I2 Connect the Channel A generator output as voltage source Vs. Set CHA to source a DC voltage of +5V ( SVMI mode ). Use Channel B as an ammeter to alternately measure I1 and I2 by connecting the lower end of R1 and R2 to CHB with CHB set to 0 V ( SVMI mode ).

Figure 3, Measuring I1 and I2

Repeat this step by using R1=R2 = 470 Ω. and write down the measurements.

b) Calculate the currents I1 and I2 by using the formulas (3) and (4).

c) Compare the results from steps 2a and 2b.

Questions:

1. How well did the measured outputs and calculated outputs compare? Explain any difference.

2. Can you apply current division to obtain I1 and I2 for the circuit shown in figure 4? Explain briefly.

Figure 4.

Figure 5 ADALM1000 test connections

The Potentiometer as voltage divider

A potentiometer is a three-terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider. The schematic symbol for the potentiometer is shown in figure 6. It is similar to the standard fixed resistor symbol with the sliding or rotating contact depicted by the arrow pointing at the body of the resistor. If voltages V1 and V2 are connected to the two fixed terminals of the potentiometer the voltage that appears at the wiper or adjustable terminal, V3, will be some value between V1 and V2. V3 will equal V2 when the rotating contact is all the way toward the V2 terminal and V3 will equal V1 when the rotating contact is all the way toward the V1 terminal.

Figure 6, Potentiometer schematic symbol

The resistance between the two fixed terminals is constant (RPOT). The resistance between the adjustable terminal and either fixed terminal will be proportional to the wiper position. If only two terminals are used, one end and the wiper, it acts as a variable resistor.

Potentiometer Design problem:

Note figure 7, for RPOT = 10 KΩ choose values for R1 and R2 such that:

V_3 = 1/3 (V_1-V_2)

When the potentiometer is adjusted all the way to one end, near bottom terminal (or the one connected to R2).

V_3 = 2/3 (V_1-V_2)

When the potentiometer is adjusted all the way to the other end, near top terminal (or the one connected to R1).

V_3 = 1/2 (V_1-V_2)

When the potentiometer is centered (half way between the extremes).

Figure, 7 Potentiometer Design problem

Build the circuit from figure 7 using your values for R1 and R2 and verify that the voltage on V3 follows the conditions set in the design problem. Use the fixed 2.5 V supply as V2 and the fixed +5 V supply as V1.

For Further Reading:

DC Voltmeter Quick Start Guide (volt-meter-tool-1.2.exe)
DC Ohmmeter Quick Start Guide (ohm-meter-vdiv-1.2.exe)
DC Meter-Source Quick Start Guide (dc-meter-source-tool-1.3.exe)

Oscilloscope Terminology

The Potentiometer

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university/courses/alm1k/circuits1/alm-cir-2.txt · Last modified: 29 Jul 2020 19:53 by dmercer